Abstract : In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically to consider the opposition between the discreet and the continuous. In this article we want to show how the widespread introduction of mathematics in physics by Galilei leas to a change in the very notion of movement. Conversely, this theorization of the movement is the origin of the elaboration of the infinitesimals, one of the major upheavals in mathematics.